Magnetoelastic Medium Research Articles

Analysis of waves subjected to mechanical force and voids source in an initially stressed magneto-elastic medium with corrugated and impedance boundary

Analysis of waves subjected to mechanical force and voids source in an initially stressed magneto-elastic medium with corrugated and impedance boundary

Anisotropy and magnetoelasticity effects on the propagation of the SH-wave-induced semi-infinite crack in a magnetoelastic orthotropic medium

The crux of the present study is to investigate semi-infinite crack propagation in magnetoelastic strip influenced by propagating SH-wave under orthotropic geometrical configurations. The Wiener-Hopf (WH) technique and two-sided Fourier integral transforms (FIT) are applied in the proposed analytical model. A closed-form expression of the stress intensity factor (SIF) has been established for the constant concentrated force. The SIF in a magnetoelastic orthotropic strip is shown to be significantly affected by the crack length and crack speed, medium anisotropy, and magnetoelastic parameter. The proposed model is compared to the case of a magnetoelastic isotropic strip in order to demonstrate the effect of orthotropy as well as other anomalies. Among other observations, it is noted that regardless of whether orthotropy exists in the strip or not, the value of the SIF rises along with the crack speed until it reaches its maximum, at which point it rapidly declines.

Interaction of a finite crack with shear waves in an infinite magnetoelastic medium

The aim of this paper is to investigate the interaction of a finite crack with shear waves in an infinite magnetoelastic medium. Fourier integral transformation is applied to convert the boundary value problem for a homogeneous, isotropic elastic material to the Fredholm integral equation of second kind. The integral equation is solved by the perturbation method and the effect of magnetic field interaction on the crack is discussed. The stress intensity factor at the crack tip is determined numerically and plotted for low frequencies. Moreover, shear stress outside the crack, crack opening displacement, and crack energy are evaluated and shown by means of graphs.

Transversely isotropic magnetoactive elastomers: theory and experiments

The current contribution is concerned with the development of novel constitutive equations for anisotropic magnetoactive elastomers (MAEs). A hyperelastic material model for an incompressible magnetoelastic medium representing transversely isotropic MAEs has been developed to investigate their response behavior in the presence of the applied magnetic field while undergoing finite deformation. Transversely isotropic MAE samples in circular cylindrical geometry with 15% iron particle volume fraction are then fabricated and experimentally tested to measure their permeability and torque–twist response. The experimental results have then been effectively utilized to identify the constant material parameters in the proposed material model. Finally, the accuracy and validity of the proposed constitutive equations are demonstrated through the comparison of the simulation and experimental results.

Reflection and refraction phenomena of shear horizontal waves at the interfaces of sandwiched anisotropic magnetoelastic medium with corrugated boundaries

The present article analyses the reflection and refraction phenomena of an incident shear horizontal wave at the lower interface of corrugated anisotropic magnetoelastic medium sandwiched between an upper self-reinforced half-space and a lower heterogeneous viscoelastic half-space. Rayleigh’s approximation method and Snell’s law are employed to obtain an algebraic equation, which is solved by the application of Cramer’s method to determine the reflection and refraction coefficients for the reflected and refracted shear horizontal waves up to first order. The boundary conditions involve the continuity of displacements and stresses at the lower and upper common corrugated interfaces of the sandwiched anisotropic magnetoelastic medium. The deduced reflection and refraction coefficients depend on various parameters, viz. width of the sandwiched layer, anisotropic magnetoelastic constants, heterogeneity parameter, viscoelastic parameter and wave number. These reflected and transmitted coefficients are computed numerically, and their variation due to the affecting parameters is illustrated graphically against angle of incidence. The critical angle and slowness section are also determined for the shear horizontal wave propagating in the considered medium. Moreover, magnitude of energy distributed among each of the reflected and refracted waves is also computed. As a special case, the obtained results are found in well agreement with the pre-established results existing in the literature.

Dynamics of Plane Waves in a Semi-Bounded Electro-Magneto-Elastic Medium

The problem of harmonic oscillations in electro-electromagnetic composites is studied. Oscillations can be initiated by the extended load vector, including the horizontal and vertical components of mechanical displacements, and electrical induction distributed on top of the surface. Boundary conditions assume full mechanical coupling for all layers of the structure. Electrical conditions on the surface top can be both electrically open, and electrically shorted. Magnetic conditions are similar to electric ones and describe the continuity of fields in between two mediums, or indicate the isolation of the magnetic field between them. The Green's function of electro–magneto–elastic medium is constructed. Phase velocities are obtained for various geometric proportions and materials.

MAGNETOELASTIC ELECTROMAGNETIC ACOUSTIC TRANSFORMATION. PART VI

In the case of EMAT using overhead transducers, a high-frequency alternating and strong polarizing magnetic fields jointly act on the magnetoelastic medium. These fields can be positioned at different directions to each other. The article analyzes the situation when the polarizing field, located along the interface of the media and the normal component of the emitter variable field are orthogonally related. That is, the classic Wiedemann effect is implemented in EMAT. It has been shown that the Wiedemann effect in EMAT contributes primarily to the generation of shear waves. The generation of longitudinal waves is secondary and less efficient. About an order of magnitude less In fact, the Wiedemann effect can only be observed (compared to the Joule effect) for the materials with low conductivity and for the ferrodielectrics. Increasing the efficiency of the method is possible by increasing the frequency of the current in the transducer. When the conductivity and frequency properly seltcted, the efficiency of the method can compete with EMAT performed by means of the Joule effect.

Influence of magnetoelasticity on frequency equation of Shear wave propagation in a multilayered magnetoelastic anisotropic monoclinic medium

The present paper deals with the Shear wave propagation in a multilayered magnetoelastic anisotropic monoclinic medium with finite difference modeling to comprehend the stability criteria, phase velocity, and group velocity. Utilizing Maxwell’s fundamental theory of magnetoelasticity, the problem has been constructed. Haskell’s matrix technique has been utilized to obtain the frequency equation. Stability analysis has been conducted based on the finite difference technique to reduce the soaring error values and control its stability. Numerical evaluation as well as graphical representation, have been employed to enlighten the effects of different values of courant number and magnetoelasticity on the phase and group velocities.

Effect of magneto-elasticity, hydrostatic stress and gravity on Rayleigh waves in a hydrostatic stressed magneto-elastic crystalline medium over a gravitating half-space with sliding contact

In this paper, the propagation of Rayleigh waves in a crystalline medium of finite thickness laid over an elastic half-space with sliding common interface is studied. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the elastic half-space is under the influence of gravity. The main aim of the paper is to establish the dispersion equation of the wave and investigate the effects of involved parameters on the phase velocity of the wave. Numerical examples for the crystalline medium, such as anisotropic Vosges sandstone, monoclinic coesite, orthotropic Rochelle salt and simply isotropic have been considered. Based on the obtained dispersion equation, effects of magneto-elastic coupling, hydrostatic stress and Biot’s Gravity parameters on the phase velocity of Rayleigh wave in the different crystalline media are analysed and illustrated graphically.

Application of magnetoelastic materials in spatiotemporally modulated phononic crystals for nonreciprocal wave propagation

In this paper, a physical platform is proposed to change the properties of phononic crystals in space and time in order to achieve nonreciprocal wave transmission. The utilization of magnetoelastic materials in elastic phononic systems is studied. Material properties of magnetoelastic materials change significantly with an external magnetic field. This property is used to design systems with a desired wave propagation pattern. The properties of the magnetoelastic medium are changed in a traveling wave pattern, which changes in both space and time. A phononic crystal with such a modulation exhibits one-way wave propagation behavior. An extended transfer matrix method (TMM) is developed to model a system with time varying properties. The stop band and the pass band of a reciprocal and a nonreciprocal bar are found using this method. The TMM is used to find the transfer function of a magnetoelastic bar. The obtained results match those obtained via the theoretical Floquet–Bloch approach and numerical simulations. It is shown that the stop band in the transfer function of a system with temporal varying property for the forward wave propagation is different from the same in the backward wave propagation. The proposed configuration enables the physical realization of a class of smart structures that incorporates nonreciprocal wave propagation.

Implementation of finite difference approximation on the SH-wave propagation in a multilayered magnetoelastic orthotropic composite medium

This paper presents an outcome of the broader effect to assess the importance of magnetoelasticity, compressive and tensile initial stress in soil dynamics. Haskell’s matrix technique is employed to investigate the SH-wave propagation in a multilayered magnetoelastic orthotropic (MMO) medium. The dispersion relation for the total (\(n-1\)) layers lying over a half-space is obtained in a closed form. Special cases are derived for both the single and double layers, and the obtained relations are found to be in good agreement with the Classical Love wave equation. Based on the finite difference technique, a stability analysis is performed to reduce the escalation of errors to make it stable and convergent. The expression for the phase and group velocities is attained by this technique when the SH-wave propagates across the MMO medium. Numerical computations and graphical exhibition have been carried out to show the effects of different values of the magnetoelastic coupling parameter, compressive and tensile initial stresses and courant number on the phase and group velocities.

Rayleigh waves in liquid layer resting over an initially stressed orthotropic half-space under self-weight

The study of surface waves (Rayleigh wave) finds their virtuous applications in a numerous geological and geophysical fields including water, oil, gas, and other subsurface geological probing and exploration. The present paper efforts to investigate the influence of initial stress, Earth magnetism, and gravity on propagation of Rayleigh waves. Considered model is consist of a liquid layer lying over a magnetoelastic orthotropic half-space under self-weight and initial stress. Method of separation of variable is used to solve the equation of motion. Solutions of governing equations are obtained in terms of displacement. Frequency relation for Rayleigh wave has been obtained and matched with classical Rayleigh wave equation. In addition to classical case, some existing results have been deduced as particular case of the present study. Obtained results have been shown through numerical illustrations. It is found that the considered parameters (initial stress, Earth magnetism, and gravity) have prominent effect on phase velocity of Rayleigh wave. Graphical representations have been made to exhibit the velocity profile of Rayleigh waves for different cases with the help of MATHEMATICA. The present study may be useful for seismologists and engineers who are concern with applications of wave propagation in magnetoelastic orthotropic medium.

Effect of Anisotropy, Earth Magnetism and Irregular Boundary on Polarized Shear wave propagation

A mathematical model is considered to investigate the behaviour of horizontally polarized shear waves (SH waves) in an irregular, heterogeneous, magnetoelastic self-reinforced medium sandwiched between two heterogeneous half- spaces. Heterogeneity in the upper half-space is due to linear variation of elastic parameters whereas quadratic variation has been considered for lower half-space. Heterogeneity in the layer is caused due to exponential variation of the parameters. The irregularity is taken in the form of rectangle. Dispersion equation for propagation of SH-waves has been obtained. Whittaker's function and the method of separation of variable are used to solve the problem.

Reflection and transmission of SH-waves at a corrugated interface between two semi-infinite anisotropic magnetoelastic half-spaces

An analysis has been carried out for reflection and transmission of a plane SH-wave incident at a corrugated interface between two anisotropic magnetoelastic half-spaces. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for first order approximation of corrugation. The expressions for reflection and transmission coefficients for first order approximation of corrugation are obtained in closed form for a special type of interface. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of magnetoelastic properties of materials of the half-spaces as well as the angle of incidence. Special cases are deduced for anisotropic and isotropic materials for particular case of corrugation. Numerical computations are performed for a specific model of two different anisotropic magnetoelastic media. The effects of anisotropic magnetoelastic coupling parameter, the angle at which wave crosses the magnetic field, frequency factor, wave length of corrugation, and the amplitude of corrugation are shown through figures.

Reflection and transmission of plane SH-waves in an initially stressed inhomogeneous anisotropic magnetoelastic medium

This study investigates the reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media. The lower half-space is considered as initially stressed and inhomogeneous. The density of lower half-space is taken exponentially varying with depth. The solutions for half-spaces are obtained analytically. The expressions for reflection and transmission coefficient are obtained in the closed form subject to continuity conditions at the interfaces of anisotropic magnetoelastic half-spaces and the Snell’s law. It is found that these coefficients depend on the initial stress, inhomogeneity parameter, the magnetoelastic coupling parameter, and the angle at which wave crosses the magnetic field of the half-spaces. Numerical computations are performed for these coefficients for a specific model of two different anisotropic magnetoelastic half-spaces. The numerical results are illustrated by the graph of reflection and transmission coefficient versus the angle of incidence. In general, as the initial stress increases the reflection and transmission coefficient increases, the affect is more prominent for more than 10 GPa. Inhomogeneity in the density of the material also increases the reflection and transmission coefficient. The anisotropic magnetoelastic parameter and the angle at which the wave crosses the magnetic field for both the half-spaces have a quite significant effect on the reflection and transmission coefficient.

Smooth moving punch in an initially stressed transversely isotropic magnetoelastic medium due to shear wave

ABSTRACTThis study investigates the effect of a semi-infinite smooth moving punch due to shear wave propagation in initially stressed, magnetoelastic, transversely isotropic material. The Wiener–Hopf technique has been employed to determine the closed form expression of dynamic stress concentration due to punch with a load of constant intensity. The substantial effects of magnetoelastic coupling parameters, horizontal and vertical compressive/tensile initial stress, and anisotropy on dynamic stress concentrations has been remarkably traced out. Numerical computations and graphical illustrations, along with comparative study, have been executed for three distinct models: when the strip is comprised of Zinc, Beryl material having hexagonal symmetry, and simply isotropic material.

The role of elastic dissipation in the formation of magnetization precession in magnetoelastic medium

As applied to the problem of reducing the noise of a rotational magnetometer, the formation of damping of magnetization precession due to elastic dissipation in magnetoelastic medium is considered. It is shown that, at a large enough elastic dissipation, the effectiveness of its contribution to the magnetic dissipation sharply decreases.

Green’s Function of Magnetoelastic Waves

The matrix (5x5) Green's function of magnetoelastic waves in an isotropic magnetoelastic medium taking into account the dipole-dipole interaction has been derived. The imaginary parts of diagonal and off-diagonal elements of the Green's function in the crossing resonance of spin and longitudinal elastic waves has been investigated. It is shown that under changing the angle of wave propagationθthe amplitudes of Green functions change drastically due redistribution of energy between the magnetic and elastic oscillation. Approximate expressions for the dependence of the widths of the gaps in the spectrum on the angleθhave been also derived.

Effect of smooth moving punch in an initially stressed monoclinic magnetoelastic crystalline medium due to shear wave propagation

This work studies the effect of a semi-infinite smooth moving punch on the shear wave propagation in an initially stressed magnetoelastic monoclinic strip. The closed form expression of dynamic stress concentration due to the punch for the force of a constant intensity has been established. The speed of moving punch associated with shear wave speed in the medium, vertical compressive initial stress, vertical tensile initial stress and monoclinic magnetoelastic coupling parameter have a substantial effect on the dynamic stress concentration owing to a semi-infinite smooth moving punch. Numerical computation and graphical demonstration has been carried out for quartz crystal with monoclinic symmetry to observe the profound effect of these affecting parameters on dynamic stress concentration. In order to highlight some of the important peculiarities of the problem, a comparative study of dynamic stress concentration in an initially stressed magnetoelastic monoclinic strip and initially stressed magnetoelastic isotropic strip has been made. Weiner-Hopf technique indicated by Matczynski has been adopted to solve the problem. In particular, some special cases have been deduced from the obtained expression of dynamic stress concentration due to the smooth moving punch.

Propagation of a crack due to magnetoelastic shear waves in a self-reinforced medium

This paper investigates the propagation of crack due to horizontally polarized shear waves in a magnetoelastic self-reinforced medium. The methodology includes the Weiner-Hopf technique. The effects of reinforcement and magnetic field on the propagation of the crack have been studied. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that self-reinforcement increases the stress intensity factor whereas magnetoelastic coupling parameter has the reverse impact. It is remarkable to state that the stress intensity factor decreases with the increase in the length of crack. Also, the comparative study has been made through graphs to find the effect of reinforcement over the reinforced-free case on the stress intensity factor. Moreover, some important peculiarities have been observed in graphs.